For plasma with anisotropic velocity distribution of particles in the form of two counter-propagating bi-Maxwellian beams, including bi-Maxwellian plasma, in the presence of external magnetic field parallel to the beams, it is shown that in a wide range of parameters, particle collisions lead to the expansion of the wavenumbers range, generally towards the long-wavelength region, and weaken the conditions for the occurrence of the Weibel-type instability. In the specified expanded range, its growth rate, found by means of solving the dispersion equation for the wave vectors orthogonal to the external magnetic field, turns out to be less than or on the order of the frequency of particle collisions. Thus, in this range of parameters, the instability development and formation of large-scale magnetic turbulence in a plasma with weak particle collisions require the long-term injection of particles with anisotropic velocity distribution.